Rewrite as a simplified fraction. ${0.6\overline{65} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 665.6565...\\ 10x &= 6.6565...\end{align*}}$ Subtracting the two equations, we have: ${990x = 659}$ ${x = \dfrac{659}{990}} $